Espaces de représentations complètement réductibles

Details Espaces de représentations complètement réductibles Espaces de représentations complètement réductibles

2009-06-19

arxiv.org/abs/0906.3750v2

Journal of the London Mathematical Society 83 (2011) pp 545-562

Mathematics

Group Theory

15 pages

Scientific paper

10.1112/jlms/jdq076

We study some geometric properties of actions on nonpositively curved spaces related to complete reducibility and semisimplicity, focusing on representations of a finitely generated group in the group G of rational points of a reductive group over a local field, acting on the associated space (symmetric space or affine building). We prove that the space of completely reducible classes is the maximal Hausdorff quotient space for the conjugacy action of G on the representation space.

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